The present invention relates to modeling the heart in medical images, and more particularly, to modeling the heart by automatically generating a statistical four-chamber heart model from 3D volumes.
Various 3D shape representation techniques are used to model the heart. One type of heart model is a volume-based heart model. Tetrahedrons are often used to represent a solid volume model. Such volume-based models are widely used in finite element based approaches to study the blood flow of a heart. Volume-based models are also commonly used in active appearance models (AAM), since an AAM models the appearance inside an object. A tetrahedral mesh (model) can be generated automatically from labeled volume data.
Another type of heart model is a surface-based heart model. Using surface-based representation, only the shape boundary of an object is modeled. Accordingly, no information about the region inside the object is contained in a surface-based model. There are many ways to represent a surface, such as a triangulated mesh, a simplex mesh (which is a dual of the triangulated mesh in topology), and a B-spline mesh (which is parametric). How to generate a good surface mesh (using as few vertices as possible to meet a predefined error tolerance) from volume data is a widely researched topic in computer graphics.
In 3D heart segmentation, surface representations are widely used in snake-based deformable models or active shape models (ASM). Deformable models are not learning based and little shape priori information is used. Snake-based approaches do not need point correspondence, so they have more freedom to evolve a shape. For example, during the shape evolution, dynamically re-meshing can be used to produce high-quality meshes. However, it is impossible for dynamic re-meshing to be used for a statistic shape-based approach, such as ASM, since the predefined topology (for example, the number of mesh points and the connection among the mesh points) cannot be changed.
FIGS. 1 and 2 show conventional surface-based heart models. FIG. 1 shows a heart model built by New York University, freely available at http://education.med.nyu.edu/courses/old/embryology/courseware/vheart/. As illustrated in FIG. 1, image 102 shows the whole heart, image 104 shows the left ventricle (LV), image 106 shows the left atrium (LA), image 108 shows the right ventricle (RV), and image 110 shows the right atrium (RA). The model of FIG. 1 is not accurate in anatomy. For example, the shape of the short axis of intersection of the RV is a crescent with two cusp points. The mesh (model) should have a sharp turn at each of the cusp points, but the model of FIG. 1 rounds these cusps. FIG. 2 shows a heart model commercially available from Zygote Media Group, Inc. at http://www.3dscience.com/3D_Models/Human_Anatomy/Heart/index.php. As illustrated in FIG. 2, image 202 shows the whole heart, image 204 shows the LV, image 206 shows the LA, image 208 shows the RV, and image 210 shows the RA. The model of FIG. 2 is built from real CT and MRI volumes, so it is more accurate in anatomy than the model of FIG. 1. However, a drawback of the model of FIG. 2 is that it is too detailed, and may contain irrelevant details for many tasks. Another drawback of the model of FIG. 2 is that the LV epicardial border is not modeled. Instead, the pericardial border of the whole heart is represented.
Another type of heart model is a statistical shape model. In order to build a statistical shape model from a group of shapes, each shape must have the same number of points and the points should have correspondence. Point correspondence refers to point i in shape A and point i in shape B corresponding to the same anatomical structure. For example, if the 99th point in shape A is the LV apex, the 99th point in shape B should correspond to the LV apex, as well. Pair-wise based approaches for establishing point correspondence are easy and fast. In such pair-wise based approaches, one shape is selected and all other shapes are matched (registered) to the selected shape. After this registration, the average of the aligned shapes is used as the mean shape. This process can be iterated to refine the mean shape. A surface mesh is then generated from the mean shape, and the surface mesh is warped toward each individual shape. Using this approach, pseudo-landmarks are sampled in a consistent way for all training shapes. In R. H. Davies, et al., “A Minimum Description Length Approach to Statistical Shape Modeling”, IEEE Trans. Medical Imaging, 21(5):525-537, 2002, a group-wise based method is proposed, in which the selection of pseudo-landmarks is formulated as an optimization problem to minimize the Minimum Description Length (MDL). A problem with this approach is that, if a dense representation is desired, the number of variables (the positions of pseudo-landmarks on each training shape) for optimization is very large. Accordingly, the optimization process is very slow and likely to converge to a local optimum.
Another approach for establishing point correspondence is to establish correspondence among shapes during the manual labeling process. This approach is relatively easy for 2D curves. Typically, only a few landmarks need to be labeled, such as points with high curvature. Uniform sampling between two neighboring landmarks on the curve will result in a dense point representation. However, it is difficult to manually label the correspondence in 3D because many more points are involved and there is no natural ordering of mesh points. In Praun et al., “Consistent Mesh Parameterizations”, In Proc. SIGGRAPH, pages 179-184, 2001, a few sparse landmarks are labeled on 3D data. Assuming that the topology (i.e., the connection between landmarks) is given, they propose a method to fit this coarse mesh to the data is a consistent way by minimizing an energy function. Since the energy function is non-linear containing multiple local optima, many heuristics are proposed to search for a good local optimum solution. However, the algorithm proposed by Praun et al., is quite complicated and the optimization step is slow.